What is the derivative of e^{cos(x}) ?

The derivative of e^{cos(x}) is -e^{cos(x)}sin(x)

What is the first derivative of e^{cos(x}) ?

The first derivative of e^{cos(x}) is -e^{cos(x)}sin(x)

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\frac{d}{d x} (e^{c o s (x)})

- e^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (e^{c o s (x)})

Apply the chain rule:

e^{c o s (x)} \frac{d}{d x} (cos (x))

= e^{c o s (x)} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= e^{c o s (x)} (- sin (x))

Simplify

= - e^{c o s (x)} sin (x)

\int x e^{b x} d x

\int sec^{5} (3 x) d x

\frac{d}{d x} (\frac{2 x y}{( 2 - x ^{2} )})

cos (6 y)

\frac{d}{d x} (\frac{a x + b}{c x + d})

What is the derivative of e^{cos(x}) ?
The derivative of e^{cos(x}) is -e^{cos(x)}sin(x)
What is the first derivative of e^{cos(x}) ?
The first derivative of e^{cos(x}) is -e^{cos(x)}sin(x)